Sorry. This is often repeated but it's simply doesn't hold up under scrutiny.
It assumes every single crewman on every B-29 that landed on Iwo would have otherwise died, which is absurd. Many of those B-29s probably would have made it back to base. Even ones that ditched would have had the crewmen rescued in most cases.
OK, let's play your "auumptions" game:
The field commanders (not even Truman!) knew we had the bomb, nor did ANYBODY knoew (in Feb '45) know if it would work, could work, or could be built.
So, with enemy airfields on IWO behind the fleet's back as they tried to land on the homeislands, why do you think that Iwo could be ignored.
How long would the air bombardment last?
Of 2400 airplanes that landed on Iwo because they were damaged/shot up, are you going to assume 80% could KEEP FLYING home? That 10% could keep flying another 5 hours to the Mariana Islands?
If 90% of those 2400 aircraft would crash (putting 21000 airmen in the water): Could even 50% have been rescued? What would happen to the bombing campaign/the mining campaign if we LOST 21,000 trained pilots and crew?